- Hướng dẫn giải

$$\begin{gathered} {\log }_2\left(1+\sqrt{x^2-5x+5}\right) \\ +{\log }_3\left(x^2-5x+7\right)=2 \end{gathered}$$

$$\begin{gathered} {\log }_2\left(1+\sqrt{1+\left(x-1\right)\left(x-4\right)}\right) \\ +{\log }_3\left(3\left(x-1\right)\left(x-4\right)\right)=2 \\ \Rightarrow \left\{\begin{array}{l}{x}_1=1\\ x_2=4\Rightarrow x_1+x_2=5\end{array}\right. \end{gathered}$$

Đáp án cần chọn là B